I forsee a problem with this idea. The sharpened edge will go right through the pizza and will damage the table surface.

Perhaps we can put our heads together and come up with some kind of solution - perhaps a disc the size of a pizza, made of something hard and cut-resistant, such as glazed, fired ceramic, that could be inserted between the pizza and the table.

Why limit yourself to pizza? You could easily apply this
technology to all sorts of other things. Loaves of bread,
for example, are notoriously difficult for the average user
to divide into individual portions, or "slices". A larger
version of this could render the task trivial. Of course,
such a device would probably be enormous, and therefore
only practical for industrial settings. Perhaps this "slicing"
could be applied at the factory, before it even gets to the
consumer.

The pizza wheel in the link provided by [Klaatu] appears to be entirely coated with (or perhaps made from) nonstick substance. That might actually explain the need for both hands; plastic isn't as sharp as steel. And so that's why I specified in this Idea that the sharp steel edge needs to remain exposed.

The funny thing is, when the cooks are away and I have to
cut my own pizza, I roll the cutter back and forth along the
line to be cut, yet the pizza mysteriously edges away from
me. I'm wondering if there's some kind of reactionless force
in action there.